UVUnwrap splitting other edges besides seams
If an edge isn't marked with a seam it will be kept together when using the standard 'Unwrap' tool as long as the geometry is connected. From your screenshot it looks like you have some extra faces between the two blue faces you have selected (the black dots are 'face-dots'), which could mean the faces aren't actually connected; outlined in red here:



Select all the faces in the mesh with A (press A again if it deselects everything) and choose Mesh> Vertices> Remove Doubles:



This will remove any vertices that are extremely close to each other and should remove those extra faces, meaning your geometry is properly connected.